| Summary: | The fundamental metallicity relation (FMR) is a postulated correlation between galaxy stellar mass, star formation rate (SFR), and gas-phase metallicity. At its core, this relation posits that offsets from the mass-metallicity relation (MZR) at a fixed stellar mass are correlated with galactic SFR. In this Letter, we use hydrodynamical simulations to quantify the time-scales over which populations of galaxies oscillate about the average SFR and metallicity values at fixed stellarmass.We find that Illustris and IllustrisTNG predict that galaxy offsets from the star formation main sequence and MZR oscillate over similar time-scales, are often anticorrelated in their evolution, evolve with the halo dynamical time, and produce a pronounced FMR. Our models indicate that galaxies oscillate about equilibrium SFR and metallicity values - set by the galaxy's stellar mass - and that SFR and metallicity offsets evolve in an anticorrelated fashion. This anticorrelated variability of the metallicity and SFR offsets drives the existence of the FMR in our models. In contrast to Illustris and IllustrisTNG, we speculate that the SFR and metallicity evolution tracks may become decoupled in galaxy formation models dominated by feedback-driven globally bursty SFR histories, which could weaken the FMR residual correlation strength. This opens the possibility of discriminating between bursty and non-bursty feedback models based on the strength and persistence of the FMR - especially at high redshift.
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